A production facility is trying to determine the best batch size for an item that is produced intermittently. This item has an annual demand of

$1$

$,$

$0$

$0$

$0$

$$units$,$ an annual carrying cost of $

$1$

$0$

$$per unit, and a setup cost of $

$4$

$0$

$0$

$.$

$$They operate

$5$

$0$

$$weeks per year, and can produce

$4$

$0$

$$units per week. What is the best batch size for this item?